MY 11 TRISECTION APPROXIMATION METHODS         Pg. 87

 

BASIC TRISECTION FORMULAS

 
tri16c.gif

FIG. 16

  Pg. 88

DESCRIPTION:

 
1. FIG. 16 above is a quarter circle showing 3Æ and its sub angles Æ
   
  with all relevant horizontal and vertical lines displayed.
   
2. All distances are measured as shown with R = 1 unit.
 

FORMULAS GENERATED:

 
1. cos3Æ = 4cos3Æ - 3cosÆ  [from CRC TABLES]
   
  cos3Æ = cosÆ(4cos2Æ - 3)
   
  Let a = cosÆ - cos3Æ - see FIG. 16, above.
   
  Let e = cosÆ - see FIG. 16, above.
   
  cos3Æ = e - 4a
   
2. cos2Æ = 2cos2Æ - 1 = 1 - 2(1 - cos2Æ) [from CRC TABLES]
   
  Let b = 1 - cos2Æ - see FIG. 16, above.
   
  cos2Æ = 1 - 2b
   
  Let d = cos2Æ - see FIG. 16, above.
    Pg. 89
  cos2Æ = 2d - 1
   
  Let c = cos3Æ - see FIG. 16, above.
   
  cos3Æ = 4cos3Æ - 3cosÆ   [from CRC TABLES]
   
  cos3Æ = 4c - 3e
   
3. sin3Æ = 3sinÆ - 4sin3Æ   [from CRC TABLES]
   
  Let p = sinÆ - see FIG. 16, above.
   
  sin3Æ = sinÆ(3 - 4sin2Æ) = p(3 - 4p2)
   
4. sin3Æ = 4sinÆcos2Æ - sinÆ = p(4d - 1)
   
5. sin2Æ = 2sinÆcosÆ = 2pe   [from CRC TABLES]
 
plane.gif
 

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